The Constructions for Large Sets and Overlarge Sets of Resolvable Hybrid Triple Systems
Received:December 11, 2013  Revised:October 10, 2014
Key Words: Hybrid triple system   large set   overlarge set   parallel class   almost parallel classes  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11471096).
Author NameAffiliation
Meihui CHENG College of Huihua, Hebei Normal University, Hebei 050091, P. R. China 
Zhifen GUO College of Mathematics and Information Science, Hebei Normal University, Hebei 050024, P. R. China 
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      An LRHTS$(v)$~(or LARHTS$(v))$ is a collection of $\{(X , {\cal B }_i):1\leq i \leq 4(v-2)\}$, where $X$ is a $v$-set, each $(X, {\cal B}_i)$ is a resolvable $($or almost resolvable$)$ HTS$(v)$, and all ${\cal B}_i$s form a partition of all cycle triples and transitive triples on $X$. An OLRHTS$(v)~ ($or OLARHTS$(v))$ is a collection $\{(Y\backslash \{y\}, \A_y^j) : y\in Y, j=0, 1, 2, 3\}, $ where $Y$ is a $(v+1)$-set, each $(Y\backslash \{y\}, {\cal A}_y^j)$ is a resolvable $($or almost resolvable$)$ HTS$(v)$, and all ${\cal A}_y^j$s form a partition of all cycle and transitive triples on $Y$. In this paper, we establish some directed and recursive constructions for LRHTS$(v)$, LARHTS$(v)$, OLRHTS$(v)$, OLARHTS$(v)$ and give some new results.
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